Sarrazin made his television debut in 1965, when Alexander Singer directed him in an episode of The Virginian. He made his feature film debut two years later in the western Gunfight in Abilene, which starred TOS guest star Emily Banks.

Sarrazin played the title roles in the comedy films For Pete's Sake (1974; with Vincent Schiavelli) and The Loves and Times of Scaramouche (his second film with Michael Forest). He also played the title role in the 1975 horror-mystery feature The Reincarnation of Peter Proud (written by Max Ehrlich and again working with Albert Henderson). He then starred in the 1976 road race comedy The Gumball Rally, along with Harvey Jason and Tricia O'Neil.

His feature film credits throughout the 1980s included Joshua Then and Now (1985) and Keeping Track, both co-starring Alan Scarfe. He later played Craig Warner in two thrillers starring Michael Caine as former Secret Agent Harry Palmer, Bullet to Beijing (1995) and Midnight in Saint Petersburg (1996). His final feature film was the 2002 horror-thriller feardotcom, which also featured Jeffrey Combs.